application with cardinality of a set

[bluemath]

Hello,

We have A and B , 2 finished sets.

And now the application f : A ---> {1, ..., card(A)}
and the application g : B ---> {1,..., card(B)}

We build A U B {1,..., card(A), card(B)}

The application h is :

x ----> f(x) (if x belongs in A)
x ----> card(A) + g(x) if x belongs in B

Actually, I don't understand this last application.
Suppose I take a x who belongs in A. What is the image of my function ? f(x) = ?

Thanks in advance

 

[Ishuda]

Hello,

We have A and B , 2 finished sets.

And now the application f : A ---> {1, ..., card(A)}
and the application g : B ---> {1,..., card(B)}

We build A U B {1,..., card(A), card(B)}

The application h is :

x ----> f(x) (if x belongs in A)
x ----> card(A) + g(x) if x belongs in B

Actually, I don't understand this last application.
Suppose I take a x who belongs in A. What is the image of my function ? f(x) = ?

Thanks in advance

Let A = {1, 2, 3, 4}, then card(A)=4 and f(1)=1, f(2)=2, f(3)=3, f(4)=4.
Let B = {a, b}, then card(B)=2 and g(a)=1, g(b)=2

Now, if x belongs to A, h(x)=f(x) and if x belongs to B, h(x)=g(x) so h(1)=1 [1 belongs to A so equal to f(1)], h(a)=4+1=5 [a belongs to B so 4+g(a)], etc.

 

[bluemath]

Many thanks for the explanation. Really clear.